In the chapters on unification in physics we have seen how mathematics provided the kinds of structures that allowed us to bring together diverse phenomena under a common framework. Yet in both the electrodynamic case and the electroweak case, the additional parameters necessary for the unification (the displacement current and the Weinberg angle, respectively) provided nothing in the way of a substantive explanation of how and why unification processes take place. My point in those chapters has been to emphasize not only the differences between the ways in which theories can become unified but also how the unification process differs from the process of explaining specific phenomena.

Initially one might suppose that this situation would be limited to physics, especially in light of its rather abstract, mathematical form. However, in this chapter and the final chapter I want to show how a unification involving biological theories has many similarities to the unifications in physics, and that many parallel conclusions about the relationship between unification and explanation can be drawn in the two cases. More specifically, I want to show how the most successful unification in biology, the synthesis between evolutionary theory and genetics, was accomplished by applying particular kinds of mathematical structures that enabled early geneticists to bring together natural selection and Mendelism under a common framework. Although a theoretical unity was achieved, there was no agreedupon explanatory model regarding the ways in which selection operated within that new synthesis. In fact, it is still an open question as to how the unification of evolutionary theory with Mendelism, under the structural constraints of population genetics, ought to be interpreted qualitatively.

Synthesis and Unity

In Chapter 6, I claimed that one of the problems with selectionist explanations was a lack of understanding of the mechanisms of heredity and variation. That difficulty was partially alleviated through the work of Gregor Mendel in the late nineteenth century, but with the rise of Mendelian genetics came a supposed conflict with Darwinian evolution. The debate was largely about the causal agents responsible for heredity and variation and about the nature of evolution itself. The controversy concerned the role of selection, as opposed to mutation, in producing changes in populations and whether evolution was gradual or discontinuous. Indeed, the issue of gradualism had a history that dated back to the publication of Darwin's Origin of Species.

Followers of Mendel saw the particulate nature of genetic factors as a basis for discontinuity in evolution and the hardness of inheritance (i.e., selection would have no effect on heritable traits). They argued that mutation pressures were the main agents of evolutionary change. Although selection was considered by Darwinians to be responsible for such change, some Darwinians claimed that individual variation was unimportant, that the causal factor in evolution was use or disuse, rather than selection. Consequently, the problems facing Darwinism included not just the origin of variation and the types of variations that were heritable but also the role of selection versus environmental conditions, which could give rise to use or disuse, the nature of species (whether they were real or abstract units) and the role of isolation in evolutionary change.

The question that occupies most of this chapter is whether or not the first word in the title – unification – bears any relation to the other two, and if so, how that relation ought to be construed. As mentioned in the introductory remarks, a common approach to fleshing out the notion of unification is to link it to explanation. A unified theory is thought to be one that can explain phenomena from different domains by showing either that the phenomena are essentially the same (e.g., light waves are simply electromagnetic waves) or that diverse phenomena obey the same laws, thereby suggesting some link between them. This explanatory power supposedly provides good evidence that the theory is true; hence, the best explanation, which typically will be the one that reveals some unity among the phenomena, should be seen as more likely to be true than its competitors. Of course, not all “best explanations” will perform a unifying function. There may be only one explanation of a particular phenomenon, and hence, by default, it will have to be considered the best. So embedded in the debate are two issues, one linking unity to explanatory power, and the other linking the concept of “best explanation” to increased likelihood of truth. This practice of drawing inferences to truth on the basis of explanatory power has been dubbed “inference to the best explanation” (IBE) and has been advocated by, among others, Harman (1965) and Thagard (1978).

More recently, however, there have been forceful criticisms by van Fraassen (1980), Cartwright (1983) and Friedman (1983) of the link between IBE and truth and its use as a methodological rule that forms the basis for inference.

“Unity” has become a much-maligned word in history and philosophy of science circles, the subject of criticism that is both normative and descriptive. The concepts of “unity of science” and “unity of method” and even the notion of a “unified theory” have been criticized for being either politically undesirable (Dupré 1996) or metaphysically undesirable (Galison and Stump 1996), or else simply nonexistent – the products of a misrepresentation of scientific practice. Critics of unity claim that when we look at scientific practice we see overwhelming evidence for disunity, rather than the coherent structure we have been led to believe characterizes science. Although some of these arguments are extremely persuasive, the desire to banish unity altogether has resulted, I believe, in a distortion of the facts and a misunderstanding of how unity actually functions in science. It is simply a mistake to deny that science has produced unified theories. So where does the evidence for disunity come from? In order to answer this question, we need to look to theory structure as a way of clarifying the nature of that unity. The task then, as I see it, is not so much one of defending a strong version of unity at all costs, but rather of providing an analysis of how it is achieved and how it functions. To that end I have chosen to focus on theory unification as the basis for my discussion of unity. Not only do unified theories provide the foundation for a more general notion of scientific unity, but also there has been a great deal of attention paid to theory unification in the philosophical literature (e.g., Friedman 1983; Glymour 1980; Kitcher 1989).

One of the themes I would like the reader to take away from this discussion is that unity, either in the broader context of science itself or in the more localized settings of specific theories, cannot be uniquely characterized. More specifically, no single account of theory unification can be given. A philosophical consequence of that claim is that unity should not be linked to truth or increased likelihood of truth; unification cannot function as an inference ticket. What exactly is the connection here? Although I have tried to explicate the features necessary for distinguishing a truly unified theory from a mere combination or conjunction, even within that framework different kinds of unity can emerge. Not only can unification exhibit a variety of ontological patterns (e.g., reductive and synthetic), but the way in which the unification is achieved can have a significant impact on whether or not there is an accompanying theoretical story, an account that can be claimed to provide a plausible representation of the phenomena. For instance, in neither the early version nor the late version of Maxwell's theory was there a viable physical interpretation of the electromagnetic field; hence, any affirmation of truth with respect to the theory would need to be severely limited in its content. Even if we consider Hertz's famous claim that Maxwell's theory was Maxwell's equations, prior to 1888 there was no guarantee that those equations were descriptively accurate, because there was no proof that electromagnetic waves existed.

In Chapter 3 we saw how Maxwell's theory incorporates two different aspects of unity: the reductive and the synthetic. We also saw the different ontological and explanatory features associated with each. In this chapter we shall look more closely at a case of synthetic unity, one that integrates the electromagnetic and weak forces. The electroweak theory provides a unified structure within which electromagnetic and weak interactions can be integrated, and yet the particles that carry the forces remain distinct. Hence, at the level of particle ontology we do not have the kind of reduction that is present in Maxwell's unification of electromagnetism and optics, where the processes are identified with each other. Yet we do have a kind of theoretical unification in terms of the gauge theory SU(2) × U(l) that describes the mixing of the two fields. In this latter sense the history is remarkably like that of electrodynamics, insofar as the unification requires the presence of a mathematical structure and a particular theoretical parameter: specifically, gauge theory (symmetry) and the Weinberg angle, which represents the combination of the coupling constants for weak and electromagnetic processes.

What makes this case especially interesting is that if theoreticians had considered only the physical similarities between electromagnetic and weak interactions that might have made them candidates for unification, it is unlikely that any such unification attempt would ever have been undertaken. But the applicability of gauge theory and symmetry principles provided a powerful mathematical framework that created not only the context but also the mechanism for generating a synthetic rather than a reductive unity of these two processes.

Although Maxwell's unification of electromagnetism and optics was, in most respects, an unqualified success, electricity and magnetism remained distinct forces within the framework of the theory. Despite the fact that they were integrated in a way similar to the synthesis of the electromagnetic and weak forces, it was not until Einstein's formulation of the special theory of relativity (STR) in 1905 that the two forces could be said to be truly unified. Indeed, it was that lack of theoretical unification that was responsible for the famous “asymmetries which do not appear to be inherent in the phenomena” (Einstein 1952a, p. 37), one of the key features that prompted Einstein's thoughts on relativity.

But the unification of two types of phenomena, electric and magnetic, in the STR was not, in and of itself, where the real power of the theory lay. In other words, the unity of electricity and magnetism was, in that case, indicative of something deeper and more pervasive – specifically, a unification of two domains of physics: mechanics and electrodynamics. In that sense, the STR, in particular the relativity principle, can be seen as both unifying empirical phenomena and unifying other theories; it functions as a kind of unifying meta-principle that extends to the whole of physics. As Einstein noted in his autobiographical remarks, “the universal principle of the special theory of relativity is contained in the postulate” that the laws of physics are invariant under Lorentz transformations from any inertial system to any other (1949, p. 57). Special relativity was what Einstein called a “theory of principle”, one that furnished constraints to which other theories had to adhere.

Maxwell's electrodynamics undoubtedly represents one of the most successful unifications in the history of science. Its demonstration that optical and electromagnetic waves travel with the same velocity and that both phenomena obey the same laws is paradigmatic of what we call the unifying power of theory. Despite enjoying some early success in Britain, there was a 15-year gap after publication of the Treatise on Electricity and Magnetism (Maxwell 1873) before Maxwell's theory was accepted on the Continent, fully supplanting action-at-a-distance accounts as the received view of electrodynamics. But even among Maxwell's British contemporaries there was by no means open enthusiasm. Sir William Thomson (Lord Kelvin) was highly critical of Maxwell's theory, despite being himself a proponent of field theoretic views of electromagnetism.

The history of the development and acceptance of Maxwell's electrodynamics is interesting from the point of view of theory unification for several reasons. First, the rather striking unification of electromagnetism and optics seems to have provided little reason to embrace the theory; even its advocates (including Maxwell himself) did not mention unifying power as playing an evidential role. To that extent the case provides a counterexample to the popular philosophical argument that unification functions to increase the likelihood that the theory is true or that it even functions as a criterion for theory choice among competing rivals. Second, the theory's development took place in several stages, the first of which depended on a mechanical aether model that was given up in later formulations.

Kepler: Unity as Mathematical Metaphysics

In the Mysterium cosmographicum Johannes Kepler claimed that it was his intention to show that the celestial “machine” was not a kind of divine living being,

His research began with a specification of certain astronomical hypotheses based on observation; that was followed by a specification of geometrical hypotheses from which the astronomical ones would follow or could be calculated. Those geometrical hypotheses were grounded in the idea that God created the solar system according to a mathematical pattern. Given that assumption, Kepler attempted to correlate the distances of the planets from the sun with the radii of spherical shells that were inscribed within and circumscribed around a nest of solids. The goal was to find agreement between the observed ratios of the radii of the planets and the ratios calculated from the geometry of the nested solids. Although unsuccessful, Kepler remained convinced that there were underlying mathematical harmonies that could explain the discrepancies between his geometrical theory and ratios calculated from observations.

Part of Kepler's unfaltering reliance on mathematical harmonies or hypotheses was based on their direct relationship to physical bodies. He considered a mathematical hypothesis to be physically true when it corresponded directly to physically real bodies. What “corresponding directly” meant was that it described their motions in the simplest way possible.

INTRODUCTION

§1. The problem of truth is one of the great classical problems of philosophy; and philosophy in its long history has given many different answers to the question of what truth is. The following considerations do not, however, concern the history of this question; rather, they examine the problem of truth from a systematic point of view. To begin with, the question at issue can be formulated in the following manner: What are the conditions for calling a proposition true; that is to say: How can one decide whether a given proposition is true or false? The examination of this problem will also permit us to respond to questions such as that of knowing whether there exist propositions which are absolutely and definitively true or whether each truth possesses a relative and provisional character – and to other questions of this kind, which are ardently discussed in philosophy. Furthermore, the envisaged inquiry will lead us to consequences which perhaps can contribute to clarifying certain points of the discussion opened in this periodical by Neurath and Petzäll – and which concerns the theory of science of the Vienna Circle.

The method by which we will attempt to establish the criteria for truth will not be that of synthetic and speculative philosophy; it will rather consist in a logical and methodological analysis of the procedures which are employed, in science, to verify a proposition; for it is only by such an analysis that one can hope to determine the character of truth in the only sense that matters for our scientific and everyday knowledge.

INTRODUCTION

This symposium is dedicated to the ideas of Moritz Schlick and Otto Neurath. I am grateful for being able to count them among those thinkers who had an essential influence on my own philosophical development.

In the fall of 1929,I participated with great interest in Schlick's seminar and in his lecture on the philosophy of nature, and I heard the debates between him and Neurath in the lively meetings of the Vienna Circle. I visited lectures given by Neurath in Vienna and later in Berlin and Chicago, and I had many stimulating, sometimes exciting, discussions with him. I think of these very different thinkers, different in temperament and philosophical style, with deep respect and gratitude.

In my contribution to this symposium, I will not evoke personal memories; rather, I will investigate the opposing views that Schlick and Neurath held on one of the major problems of epistemology.

The problem I have in mind is the question under which conditions – or given which reasons – should we accept empirical statements, especially the statements of the empirical sciences. I will call Schlick's and Neurath's views foundational and coherentist, for short.

Both Schlick and Neurath were empiricists. In the brochure “The Scientific Conception of the World: The Vienna Circle,” which was published in honor of Moritz Schlick by Carnap, Hahn, and Neurath in 1929,2 the basic conviction of the group is said to be “empiricist and positivist: there is knowledge only from experience, which rests on what is immediately given. This sets the limit for the content of legitimate science.”

INTRODUCTION

Science is often said to be a search for truth, a quest aiming at the formation of true beliefs about our world – beliefs concerning particular facts was well as general laws that may connect them.

But however appealing this conception may seem, it has, first of all, fundamental logical flaws, and second, it fails to do justice to a group of considerations that govern the critical appraisal and the acceptance or rejection of hypotheses and theories in science.

I propose briefly to elaborate this claim and to suggest an alternative way of characterizing science as a goal-directed endeavor.

The following considerations are informed both by the ideas of logical empiricism and by the more recent methodological explorations in a pragmatic-sociological vein undertaken by Thomas Kuhn and by kindred thinkers.

SCIENTIFIC THEORIZING: INVENTION AND CRITICAL APPRAISAL

Scientific theories are introduced in an effort to bring order into the diversity of the phenomena we encounter in our experience. How are such theories arrived at, and how are they supported?

Devising of effective theories is not a matter governed by systematic rules of discovery. As Einstein was fond of saying, scientific hypotheses and theories are arrived at by free invention, by the exercise of a creative scientific imagination. But their actual acceptance in science is subject to a critical evaluation by reference to the results of experimental or observational tests and to certain important additional criteria, which will be considered shortly.

Rudolf Carnap was the leading figure among the originators and the moving spirits of the stream of philosophical thought known as logical positivism or logical empiricism. Carnap preferred the latter name: The appellation “empiricism” rather than “positivism” was to set the movement apart from earlier forms of positivism, and the term “logical” was to call attention to the great importance this new empiricism attributed to the concepts and methods of contemporary logic as tools of philosophical analysis.

In Carnap's work, logic loomed large not only as a tool but also as a subject of philosophical investigation. A great deal of his research was devoted to problems in logic and metalogic, including the fields of logical syntax and semantics; the results of this work comprise substantial contributions to deductive logic as well as the most comprehensive and rigorous system of inductive logic yet devised.

The papers of my colleagues on this symposium address themselves to Carnap the logician; let me, therefore, attempt a brief appreciation of Carnap the logical empiricist philosopher.

Carnap's work outside the field of logic was devoted almost exclusively to epistemology and the philosophy of science, and his principal contributions to these fields are united by a common leitmotiv – namely, the search for ever more careful and philosophically illuminating reformulations, or explications, of the basic idea of empiricism that all our knowledge of the world ultimately derives from what is immediately given to us in the data of our direct experience.